Currently, when developing twitch extensions, the local test mode does not work in firefox. This can be fixed by adding the "loopback-network" permission to the outer supervisor-ext iframe, making the allow list allow="loopback-network encrypted-media *" - this will allow the browser to request access to local resources if they are accessed, such as the dev iframe.
More info about this security feature can be found at https://developer.mozilla.org/en-US/docs/Web/Security/Defenses/Local_network_access - adding this to the iframe delegates permission for accessing local resources to the parent scope, which allows the prompt to work and local access to actually pass through.

An example in the TwitchDev discord of this working, by setting the permission and clearing + re-adding the src to the iframe to force a reload: https://discord.com/channels/504015559252377601/523676096277905419/1533659031141351477

This is a fairly quick fix that completely fixes the local test mode of extensions, since that broke after firefox added tighter security features for accessing local resources, without inherently weakening security (people don't get this prompt unless the supervisor requests access - you aren't adding it to the actual extension iframe, so other extensions can't then request local access to resources themselves)